Optimally Resilient Strategies in Pushdown Safety Games Joint work - PowerPoint PPT Presentation

Optimally Resilient Strategies in Pushdown Safety Games Joint work with Daniel Neider (MPI-SWS) and Patrick Totzke (Liverpool) Artwork by Paulina Zimmermann Martin Zimmermann University of Liverpool August 2020 MFCS 2020 Martin Zimmermann University of Liverpool Resilient Strategies in Pushdown Safety Games 1/10

Reactive Synthesis Automatically generate correct-by-construction systems. Martin Zimmermann University of Liverpool Resilient Strategies in Pushdown Safety Games 2/10

Reactive Synthesis Automatically generate correct-by-construction systems. Martin Zimmermann University of Liverpool Resilient Strategies in Pushdown Safety Games 2/10

Reactive Synthesis Automatically generate correct-by-construction systems. Martin Zimmermann University of Liverpool Resilient Strategies in Pushdown Safety Games 2/10

Reactive Synthesis Automatically generate correct-by-construction systems. Martin Zimmermann University of Liverpool Resilient Strategies in Pushdown Safety Games 2/10

Reactive Synthesis Automatically generate correct-by-construction systems. Martin Zimmermann University of Liverpool Resilient Strategies in Pushdown Safety Games 2/10

Reactive Synthesis Automatically generate correct-by-construction systems. Martin Zimmermann University of Liverpool Resilient Strategies in Pushdown Safety Games 2/10

Reactive Synthesis Automatically generate correct-by-construction systems. Martin Zimmermann University of Liverpool Resilient Strategies in Pushdown Safety Games 2/10

Reactive Synthesis Automatically generate correct-by-construction systems. Martin Zimmermann University of Liverpool Resilient Strategies in Pushdown Safety Games 2/10

Reactive Synthesis Automatically generate correct-by-construction systems. Martin Zimmermann University of Liverpool Resilient Strategies in Pushdown Safety Games 2/10

Reactive Synthesis Automatically generate correct-by-construction systems. Martin Zimmermann University of Liverpool Resilient Strategies in Pushdown Safety Games 2/10

Reactive Synthesis Automatically generate correct-by-construction systems. Martin Zimmermann University of Liverpool Resilient Strategies in Pushdown Safety Games 2/10

Reactive Synthesis Automatically generate correct-by-construction systems. Martin Zimmermann University of Liverpool Resilient Strategies in Pushdown Safety Games 2/10

Reactive Synthesis Automatically generate correct-by-construction systems. Model the interaction between a system and its environment by an infinite-duration zero-sum game on graph. The winning condition captures a specification of the system. A winning strategy for the system player corresponds to an implementation satisfying the system specification. Martin Zimmermann University of Liverpool Resilient Strategies in Pushdown Safety Games 2/10

Reactive Synthesis Automatically generate correct-by-construction systems. Model the interaction between a system and its environment by an infinite-duration zero-sum game on graph. The winning condition captures a specification of the system. A winning strategy for the system player corresponds to an implementation satisfying the system specification. Martin Zimmermann University of Liverpool Resilient Strategies in Pushdown Safety Games 2/10

Reactive Synthesis Automatically generate correct-by-construction systems. Model the interaction between a system and its environment by an infinite-duration zero-sum game on graph. The winning condition captures a specification of the system. A winning strategy for the system player corresponds to an implementation satisfying the system specification. Martin Zimmermann University of Liverpool Resilient Strategies in Pushdown Safety Games 2/10

Reactive Synthesis Automatically generate correct-by-construction systems. Model the interaction between a system and its environment by an infinite-duration zero-sum game on graph. The winning condition captures a specification of the system. A winning strategy for the system player corresponds to an implementation satisfying the system specification. Martin Zimmermann University of Liverpool Resilient Strategies in Pushdown Safety Games 2/10

Reactive Synthesis Automatically generate correct-by-construction systems. Model the interaction between a system and its environment by an infinite-duration zero-sum game on graph. The winning condition captures a specification of the system. A winning strategy for the system player corresponds to an implementation satisfying the system specification. Martin Zimmermann University of Liverpool Resilient Strategies in Pushdown Safety Games 2/10

Reactive Synthesis Automatically generate correct-by-construction systems. Model the interaction between a system and its environment by an infinite-duration zero-sum game on graph. The winning condition captures a specification of the system. A winning strategy for the system player corresponds to an implementation satisfying the system specification. Martin Zimmermann University of Liverpool Resilient Strategies in Pushdown Safety Games 2/10

Reactive Synthesis Automatically generate correct-by-construction systems. Model the interaction between a system and its environment by an infinite-duration zero-sum game on graph. The winning condition captures a specification of the system. A winning strategy for the system player corresponds to an implementation satisfying the system specification. Martin Zimmermann University of Liverpool Resilient Strategies in Pushdown Safety Games 2/10

Reactive Synthesis Automatically generate correct-by-construction systems. Model the interaction between a system and its environment by an infinite-duration zero-sum game on graph. The winning condition captures a specification of the system. A winning strategy for the system player corresponds to an implementation satisfying the system specification. Martin Zimmermann University of Liverpool Resilient Strategies in Pushdown Safety Games 2/10

Resilience in Safety Games Dallal, Tabuada and Neider : Add disturbances edges to model non-antagonistic external influences. Question: How many disturbances make the system player lose? Martin Zimmermann University of Liverpool Resilient Strategies in Pushdown Safety Games 3/10

Resilience in Safety Games Dallal, Tabuada and Neider : Add disturbances edges to model non-antagonistic external influences. 0 Question: How many disturbances make the system player lose? Martin Zimmermann University of Liverpool Resilient Strategies in Pushdown Safety Games 3/10

Resilience in Safety Games Dallal, Tabuada and Neider : Add disturbances edges to model non-antagonistic external influences. 1 0 Question: How many disturbances make the system player lose? Martin Zimmermann University of Liverpool Resilient Strategies in Pushdown Safety Games 3/10

Resilience in Safety Games Dallal, Tabuada and Neider : Add disturbances edges to model non-antagonistic external influences. 1 0 1 Question: How many disturbances make the system player lose? Martin Zimmermann University of Liverpool Resilient Strategies in Pushdown Safety Games 3/10

Resilience in Safety Games Dallal, Tabuada and Neider : Add disturbances edges to model non-antagonistic external influences. 1 0 2 1 Question: How many disturbances make the system player lose? Martin Zimmermann University of Liverpool Resilient Strategies in Pushdown Safety Games 3/10

Resilience in Safety Games Dallal, Tabuada and Neider : Add disturbances edges to model non-antagonistic external influences. 2 1 0 2 1 Question: How many disturbances make the system player lose? Martin Zimmermann University of Liverpool Resilient Strategies in Pushdown Safety Games 3/10

Resilience in Safety Games Dallal, Tabuada and Neider : Add disturbances edges to model non-antagonistic external influences. ω + 1 ω + 1 ω + 1 2 1 0 2 ω + 1 1 ω + 1 Question: How many disturbances make the system player lose? Martin Zimmermann University of Liverpool Resilient Strategies in Pushdown Safety Games 3/10

Resilience in Safety Games Dallal, Tabuada and Neider : Add disturbances edges to model non-antagonistic external influences. Theorem (Dallal, Neider & Tabuada, 2016) A safety game with n vertices has resilience values in { 0 , · · · , n − 1 } ∪ { ω + 1 } . The resilience values and an optimally resilient strategy can be computed in polynomial time. Martin Zimmermann University of Liverpool Resilient Strategies in Pushdown Safety Games 3/10

Systems with Infinite State Space Pushdown graphs are configuration graphs of pushdown automata. One-counter automata are pushdown automata with a single stack symbol (that can still test the stack for emptiness). ⊥ A ⊥ A 2 ⊥ A 3 ⊥ A 4 ⊥ A 5 ⊥ q I · · · q 1 · · · q 2 Martin Zimmermann University of Liverpool Resilient Strategies in Pushdown Safety Games 4/10

Systems with Infinite State Space Pushdown graphs are configuration graphs of pushdown automata. One-counter automata are pushdown automata with a single stack symbol (that can still test the stack for emptiness). ω + 1 ω + 1 ω + 1 ω + 1 ω + 1 ω + 1 · · · · · · 0 1 2 3 4 5 0 Martin Zimmermann University of Liverpool Resilient Strategies in Pushdown Safety Games 4/10